Quadratic Equations

A quadratic equation is written as

A quadratic equation is written as ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0. For example, 2x² - 5x + 3 = 0 has a = 2, b = -5, c = 3.

A root (or solution) of ax²

A root (or solution) of ax² + bx + c = 0 is a value of x that makes the equation true. If α is a root, then aα² + bα + c = 0. For example, x = 2 is a

This method involves expressing ax² +

This method involves expressing ax² + bx + c as a product of two linear factors. Steps: 1) Find two numbers that multiply to give 'ac' and add to give

For ax² + bx + c

For ax² + bx + c = 0, the roots are x = (-b ± √(b² - 4ac))/2a. This universal formula works for any quadratic equation. Example: For x² - 4x + 3 = 0,

The discriminant D = b²

The discriminant D = b² - 4ac determines the nature of roots: If D > 0: two distinct real roots, If D = 0: two equal real roots, If D < 0: no real roo